I happen to be someone who carries a camera with me all the time. So I am doing some various side by side shooting to see some of the performance issues each presents. The first item would be resolution. A high number of megapixels does not mean resolution and sharpness will be impressive. Then again what are the images needed for? Web sharing - then almost anything works. The real obvious differences here when looking at full images are the details in fine areas like the leaves. The smaller sensor shows more smearing of the scene. There is also a greater tendency to blowout highlights as you'll see. So it really depends on what the files will be used for. Larger prints or cropping in - may be a problem. Here are some quick samples of an iPhone 5 vs a FinePix XS-1 and X20 which have a 2/3" sensor. Click to enlarge images.
FinePix XS-1 images below
The long zoom option is handy. This shot of the climber is from the rocks on the pic below it. 24-624mm zoom.
These folks are resting in the rock shadow area above.
Fujifilm X-Pro1 Images vs iPhone